Nsio explains: Perspective

Seventh tutorial in my Nsio explains series. I'm finally talking a little about the infamous perspective. You can't really get away from it.

Consider this as my Christmas present to the dA community!

Isometric vs. perspective, 2D vs. 3D:

I guess everyone knows how to draw a cube at least to some extent. The question is whether that cube has successful depiction of three dimensional illusion.

I, for one, drew a lot of cubes in isometric projection and I thought it was three dimensional. But it's not. In fact, it looks very weird, if you think about it. You may look at this example as well: dsearls.org/courses/C122CompSc… . In orthogonal projections, the sides of the cube are always parallel. And in a sense, it's right, the sides of the cube needs to be parallel so that it would be a cube. However, the sides aren't parallel at all in perspective drawing. The cube is skewed, but for us, it looks even more like a cube than before.

Our brains won't bother processing this skewed look around us, because it doesn't have to. You simply know that thing which actually looks skewed is a cube with right angles and straight sides. That said, you don't probably even realize how weird and distorted the world looks around yourself. And when you attempt to draw a cube, you might draw an isometric projection of it and call it 3D, because that's how it really is right? Well, while it's true, it's not what we actually see when we look at a cube in three dimensional space. So in order to draw a successful illusion of three dimensions, you have to draw the cube "wrong" in order to make it look like how we would see it in reality.

I understand the difference between 2D and 3D as I have drawn in my examples. If the cube drawing is truly 3D, there shouldn't be any doubt about the orientation of it's faces. However, if you draw and isometric cube, there are two possibilities: there is either normal cube or inverted cube. The faces of the cube can either face outwards or inwards. You can force your mind to see an inverted image of three dimensional cube, but if you can do that, you will see something totally weird and your brains can't probably comprehend what it is seeing. When I do this, I see the cube "inflating" back to normal the moment I see it inverted.

As a big fan of optical illusions, I suggest looking at this illusion too: www.lhup.edu/~dsimanek/3d/stai… . Pay attention how the guy is sitting on the stairs.

Why things look small at distance?

Because they are far away? True, but I have a bit different way to approach this question. I understand this phenomenon trough field of vision. You see, you could consider that our eyes are the point of a hollow cone and the field of vision expands as the cone gets larger. When you look very far, the cone has extended very far too. Now, if you place a wall right in front of you, your field of vision can't accommodate that wall, so it appears very large and you can't see anything else. If you step back, you eventually begin to see the surroundings around the wall. The wall appears to have shrunk before your eyes. If you keep walking backwards, the portion of the surrounding get larger in comparison to the wall. Finally, the difference between the surroundings and the wall that fill your field of vision is so great, that the wall basically disappears from your view. And despite becoming so small that it's hardly visible, it's size is still the same.

They Eye-level:

(You may know the term of horizon. It's good to note that when we talk about horizon in perspective, it's not necessarily the same as the physical horizon!)

When you are about to draw a perspective, you need to decide where the intended beholder is located and where she is looking at. The horizon of the perspective determines the eye-level. Then the position of the objects in relation to the horizon determine how the beholder sees the scene. For example, if the beholder's eyes are close to the ground, the objects dominate the topside of the horizon and usually the horizon is placed rather low on the canvas (the position of the horizon on the canvas doesn't really matter, but if you are going to draw a lot of sky, you will want to draw it rather low to actually be able to show the sky).

It's good to note that when a person (or any object) farther away and a person (or any object) with same height are seen at the same time, the horizon cross them exactly at the same place. That said, if you draw a person so that the horizon line crosses him around the chest, then all persons with the same height farther away also have the horizon line around their chest. When you have persons with different heights, then it will get a bit trickier, but it's still can be done by following the same principles. Be careful when you place people in perspective. Failing to follow the rules will result in rather interesting effects. The same person may appear as a dwarf or a giant depending on how you draw him in relation to the horizon!

Drawing Perspective:

In order to draw a successful perspective, you will need to know how the things get skewed according the perspective. For that, you will need to know how to use the horizon, vanishing point(s) and perspective guidelines. When you are drawing perspective, you will use these tools to construct convincing perspective. (Note, I'm not going to explain how to actually construct a perspective, but rather explain the idea behind the perspective).

To put it short:

1)The horizon line determines the eye-level

2)The vanishing point is located on the horizon line (as the name suggest, things disappear at the vanishing points, just like I told about the field of vision earlier).

3)The guidelines meet at the vanishing point (These determine the direction towards the vanishing points, so that you know how to skew your drawing).

one-point-perspective:

As the name suggests, there is only one vanishing point in this perspective. It's most often located directly in front of the beholder. This kind of perspective suits mostly on indoor corridors or in some street views. But in general, this perspective is rather limited: the farther you go from the vanishing point in any direction, the perspective becomes distorted. Note, that all vertical and horizontal lines are parallel, only the lines going towards the vanishing points aren't.

two-point-perspective:

This perspective kind of fixes the issue mentioned in one-point-perspective. Now there are two vanishing points and only vertical lines are parallel. This kind of perspective is pretty useful for many scenes already. The higher or lower you go from the horizon, the more distorted the drawing becomes.

Placing the vanishing points too close to each other is the most common perspective mistake. If you are drawing a house on A4 paper, the vanishing points are far outside the paper boundaries. If you draw the vanishing point within the paper, you respectively need to draw the object in perspective smaller.

three-point-perspective:

Third vanishing point isn't added on the horizon, but above or below instead. Now none of the lines are parallel. This eliminates the distortion in vertical axis to some extent. This perspective allows the beholder gaze up to the sky or downwards. Note that you can't get both, because the perspective guidelines will cause the tremendous distortion the farther you go from the third vanishing point.

The third vanishing point is often placed very far from the horizon. The farther it is from the horizon, the more subtle the vertical skewing is.

The Fisheye perspective:

All the three methods thus far make use of straight lines. When fourth and fifth vanishing points are introduced, there are no longer straight lines. This is due to fisheye effect taking place which causes all the lines curve. This is pretty tricky to construct, but that's very close to how we actually see the things around us (www.2d-digital-art-guide.com/m… this is where I grabbed the spherical perspective grid).

The problem with perspective drawing is the fact that you can only draw what's in front of you. In perspective drawings, the beholders view is sort of "locked" so you can't look what's on the left or right . There is six-point perspective, where the sixth vanishing point is located behind the beholder and it's possible to draw 360 degree view of the scene. This is already getting so ridiculous, that it's not really worth the trouble. Besides, I believe it's possible to draw perspective close enough without constructing the perspective. Even though I'm saying this, it's still crucial to know how the things I have explained work in order to draw the perspective right.

When I draw perspective, I rarely really construct them. Instead, I'm imagining how I would see the scene around me if I was to look around. Remember, that you can't draw the guidelines randomly in any perspective. You will still need to know how the objects looks from certain point of view. That said, I'm trusting more my own eyes and use the guidelines only when I really need them.

So to get started with a perspective drawing, I usually draw some sort of reference object first. I'm not really thinking the angle at this point, I'm just drawing an object that looks three dimensional. When I have drawn this object, I will begin to "look around" the canvas. I'm trying to see the "where" I had drawn the reference object in relation to the beholder. And that's how I keep working on the drawing, finding the relations between the elements according to the reference object and the beholder. I may still use the guidelines every now and then, but mostly I'm just trying trust my understanding of how I will see the objects around me.

Same goes with basically anything I draw. When I draw human characters, I usually draw them as if they were rather close to the beholder. That's why the feet are seen from above. And if they eye-level is around the waist, then the head is seen from below. It's also good way to show the height of the character in relation to the beholder, as shorter characters need to look upwards and taller characters downwards in order to look the beholder's face. This then can be used in manga to help the reader feel like she was part of the story.

Foreshortening has a lot to do with the perspective, but I decided to leave it out for now.

I have to ask you this, how should you treat the perspective guidelines when constructing it? I am having a lot of trouble associating it's purpose other than defining the idea that something vanishes to a point, this very fact is limiting me in creating certain poses that I want in two point perspective.

Is it necessary to construct figures in a box for it to be correct? I find it hard to draw a shape within a shape and it makes me feel like I have limited space to work with.

Also if I want to draw things more to the side of the canvas like it being more present on the left than the center for composition purposes, does it mean that I need to extend my vanishing points further apart from each other to prevent distortion? Thanks in advance, I might follow up with some more questions regarding this so sorry if I clog up the comment section

Guidelines that meet at the same vanishing point are always parallel. What do we know about a box? Choose one edge and all the edges that are parallel with it will meet at the same vanishing point. So although the lines drawn from one vanishing point looks like a fan, they are parallel with each other and always will be.

What else do we know about a box? The rest of the edges that aren't parallel with the edge you chose are perpendicular to these lines, either horizontally or vertically. Apply the same rule as above and you will have new guidelines receding towards two different vanishing points. Two point perspective just doesn't take in account the third vanishing point that's either above or below because it's a simplification of the real perspective.

That said, if the third vanishing point could be either above or below, that means that there are actually two vanishing points at the either end of the vertical axis. See this animation I made and see yourself:Cube demo . If this is true, which btw is, then the same rules has to apply to the other vanishing points and guidelines. That makes 6 vanishing points in total, two for each axis. You just cannot see the effect of the other vanishing points and in two point perspective it is assumed that there aren't more than two vanishing points. If you can see the effect, then the guidelines have to curve in order to look right on a two dimensional canvas. They will still follow the same rules and these guidelines are still straight, but this distortion just has to take place. At this point the whole point of constructing perspective is lost because you will no longer be able to use straight lines that are easy to work with. This is how everything really looks though.

I don't know what you are trying to achieve with your poses, but you need to consider the fact that two point perspective works only in very limited area. Thus it's possible that you are trying to do something that just is beyond the limitations of the two point perspective. If you move the vanishing points farther away, you will only flatten the perspective, but you won't be able to physically position the object to the left unless you take in account the vanishing point that's on the other end of the axis (which leads to panorama view like this: www.fortlauderdaleobserver.com… ). However, you can decide how to frame the scene you are drawing, so that the object is on the left portion of the canvas. The whole perspective system doesn't need to fit within the canvas or the frame

You don't have to draw objects within a box, but do you get the benefits of the box now that I told you how the guidelines and vanishing points are related to it? The edges of the box are easy to read, which makes it the best possible reference for drawing anything else within the perspective. It's easier to use the box as a reference if the object is inside because the guidelines are closer to the object you are drawing. Nothing prevents you from drawing the object next to the box though. That will just require more eyeballing when there are no guidelines nearby to refer to.

Thanks for the response, what I am trying to achieve with the pose is the character kneeling but I want to show more of the face and fit the body in as well, I find it hard to show the front of the character which lead to my question regarding the guidelines.

Here's my theory that I tried to work out for the problem, if I want to show more of the front of the character but still have the 2PP affect I'll need to move the vanishing point that is on the left more towards the canvas and move the one on the right further away because we are taking into account the axis at which it is placed. So logic says that if I move the left vanishing point more towards the canvas we'll see the front side of the cube more and less of the left side of it which is what I am trying to accomplish.

Now the reason I asked about the guidelines isn't because I don't understand the rules of it but more because I don't understand how to use it to my advantage, my thought process when I use two point perspective is that no matter what I'll always see the side of the object and less of the front because the object is rotated in space so the middle line that divides the cube into two edges that lead to different vanishing points is kind of confusing to me, do I draw the figure in the middle where the middle line of the cube is or do I decide which side of the cube the object is facing?

For example, what I am referring to let's take a sphere as a reference, I draw a cube in two point perspective and put a sphere inside of it, do the guidelines determine how the plane of the sphere appears? Let's say that the left side of the sphere is visible and it is the front, so anything on the second vanishing point tells me it's either right or left side of the sphere?

I feel limited in a sense when thinking about how much I want to show and what angle I want the perspective be at, I'll try to simplify my question into fewer words because I think I am confusing myself when asking it or misinterpreting the meaning of the question.

Do the guidelines necessarily determine what sides of an objects are visible to the viewer?

The situation you are trying to draw is nearly identical to one point perspective. You probably didn't have the other vanishing point within the canvas and the character wasn't close to it, and the other vanishing point wasn't far enough. You could draw the character along the diagonal you specified though, but then there isn't much point in the box. Basically you would just have a character that is tilted 45 degrees from the perspective system determined by the box.

The two vanishing points that you are using are at the end of the x and y axis, respectively. If both vanishing points are outside of the canvas and equally far away from the point you are looking at, you have a classic example of two point perspective. You are right, if you move either of the vanishing points closer to the canvas, i.e. the center point of your view, the other vanishing point will move further away. But in reality, the vanishing points aren't moving along the canvas. They are circling around you. The moment one of the vanishing points is directly in front of you, then the other is directly on to your right (and left). If you turned your head 90 degrees, you would see that vanishing point in front of you. That's why the horizon isn't really a line, it's a circle and since you are in the middle of it, it appears to look just like a straight line.

In an event where all guidelines receding to this other vanishing point are truly parallel on the canvas (meaning that it's impossible for them to meet at vanishing points because that's what being parallel effectively means). If the lines cannot meet, then the vanishing point is infinitely far away. You get a one point perspective.

Tilt the view slightly and you will have a two point perspective again. However, since the difference is so small, it's hardly visible. This is the power of one point perspective: you can ignore the effects of the other vanishing points. Once the difference becomes clear, i.e. you tilt the viewing angle more, one point perspective will not work any more, but two point perspective will still get the job done.

So yes, the guidelines coming from one vanishing point will determine the planes that you can see. The intersection between two lines from two different vanishing points are in 90 degree angle. If you draw the two vanishing points on the same canvas and try to draw a situation where guidelines coming from one vanishing point are truly parallel, you will notice that you can't do it. The guidelines are all going along the horizon which means the box will be infinitely far away. If you zoom in to the infinity to see this cube, then the other vanishing point will be infinitely far away instead. If this doesn't happen, you have drawn a skewed perspective and you are breaking the rules.

Thank you for taking your time and answering my questions, I will examine the advice you gave me and work on top of it to achieve the angle that I want, I was a little bit scared to use one point in my case because I thought it might look a little bit weird to have the character in that perspective system but I can visualize how it could work out now. Thanks a lot!

I have a question, how do you go about deciding what kind of perspective you will use? because I find it kind of difficult especially with the human form to decide how to set up the angle and what vanishing points to use, my main problem is deciding when to shift from using one point and two point perspective.

I feel like what's missing in tutorials regarding perspective is how to manipulate them to your own interest which is what I am struggling with right now, if you could give some tips it would be nice.

The skill comes trough practice and experience. When I draw, I have a feeling what kind of perspective and viewing angle will serve the drawing the best. I suggest using some manga comics as references to get ideas what kind of decisions the artists have done.

Note that there is always a vanishing point in front of you. Then there are one on the left and right, above and below and even behind you. So six vanishing points in total and each time you look straight at one of them, it's directly in front of you. The amount of vanishing points influencing the drawing depends on how much you want to show within the canvas. But, in order to fit the left and right vanishing points in the same drawing, the perspective has to bend. That's because left and right vps are on the same axis and if you want to show the both ens so that the vanishing points are in front of you, this distortion has to take place.

This is panorama effect. However, I suggest that you don't try this kind of advanced perspective just yet.

Each object within the perspective can have different vanishing points depending on their orientation. If the object is on your eye level or only slightly above or below, you can ignore the influence of the vps above and below. The further up or down you place the object from your eye level, the more the respective vanishing points will influence the drawing.

However, you are in point where it's most beneficial to keep the perspective and character drawing practices separate from each other. Practice perspective with basic boxes because applying perspective on complex forms is difficult until the point you can see important visual cues and imagine them within a box. But for example, lines drawn along the shoulders and hips will meet at the same vanishing point if the torso is straight. So in the end it's only about aligning the body parts according to your chosen perspective. But in order to be successful at that, you have to know how the body looks and behaves and where to put it in perspective system to make it work. Drawing perspective isn't difficult, but drawing a specific perspective is difficult because there are so many things to consider.

I have one more question regarding the rule where an object that faces a different direction has its own vanishing points. Now when you draw something in two point perspective or three point, how many vanishing points would you give an object that is facing a different direction? should it be equivalent to the amount of the systematic vanishing points or should you just give it one separate one? Thanks in advance.

Technically the object needs all the 6 vanishing points at any time. If you have two cubes in the scene where you have rotated them along vertical z axis, the vanishing points above and below will still coincide and you won't need additional vps there. If they have completely different orientations, then both of them have their own vanishing points.

However, you also need to take in account that these cubes exist in world that has a horizon which I call "global perspective". As long as the bottom plane of the cube is also horizontal, the vanishing points will be on the horizon. The moment you rotate the cubes, their vanishing points will no longer coincide with the global perspective. You could say that these cubes now follow respective sub-perspectives have their own horizons, but they are still within the global perspective. That said, they sill follow the exact same rules within the global perspective, but you won't be able to utilise its vanishing points to construct them. The power of perspective system is in its simple rule: all lines that are parallel to each other meet at the same vanishing point, period. When the objects don't have any lines that coincide with the global perspective, you can't use it's perspective system to construct them. That's where sub-perspective and additional vanishing points will kick in.

A typical example of global perspective is your room. The furniture and objects in your room may have their own sub-perspective systems but they most likely coincide with the orientation of your room (shelves are along the walls etc). Thus, you can construct your room with just few vanishing points. Throw your chair and stop the time, and you will have a scene where the chair won't follow the perspective determined by the room

As I said, there is always a vanishing point in front of you, or rather, wherever you are looking at. That also means that there is always a "horizon" where you look as well. You could imagine that you are within a sphere, which consists of a point cloud full of vanishing points and horizons for every need. Global perspective is just one of them, the most important one only because we refer to the ground plane thanks to gravity.

Hi, Regarding 2D perspective, if i wanted to draw a cube or rectangular prism at different perspectives, without zooming in or out, just moving the object up down left right (not rotate), HOW do the lengths, widths, and heights relate to each other? If based on a cube, is the width always greater than the length? Is there any relation to the foreshortening, as in if I moved the cube up or down, would the original height line decrease? And since we are able to see the top/bottom plane of the cube, would that have any relation to the height line decrease. Finally, am I complicating this stuff too much and should just rely on practice?

Unless you add new vanishing points to the right, left, up or down respectively, the object your are moving will become skewed.

The behavior you are looking for can be tested with two point perspective by drawing some cubes between the vanishing points in different places. Remember that if at any time you see one of the faces head on, there is a vanishing point in front of you (the sides are obviously receding to that point so you won't see them).

Now, if you start moving the cube to the right, the side from the left emerges, becoming wider the more you move to the right (while the front face width become narrower. When you are in the middle point between the vanishing points, the front and left face are equal in size and shape. If you keep moving, the procedure is the same, but "reversed". In other words, when you reach the vanishing point on the right, the face on the left will become the new front face. This exactly same thing happens with up and down, with respective faces becoming visible or hidden.

That said, the more you see one face of the cube, the less you will see other faces. That will also mean that the longer the edges are on the front face, the shorter they will be on the side faces, especially those edges that recede towards the vanishing point. So yes, if we see top/bottom face of the cube, it will have an effect on the foreshortening

To take in account the real behavior in perspective, if you keep moving an object in one direction, the farther away it will go from the beholder. That said, you won't be able to keep the object size the same unless you keep zooming in while you move it. If the beholder doesn't move, or the object doesn't orbit the beholder, the object will disappear once it reaches the other vanishing point because of the distance. In order to do this in 2D perspective, the guidelines need to curve so that the object won't become skewed.

You aren't complicating this, you are doing just the right thing by addressing the rules that you will need to understand in order to be successful in perspective. They are sort of complicated, yet so straightforward and simple. Once you understand the rules and you practice enough, you don't need to think in such complicated way because you will feel it.

Thank you for the quick reply.So what you say makes a lot of sense, but is there an application or program I can use to try this out? I've been using sketch up but I noticed that in perspective mode, there is no foreshortening of the vertical lines when the eye line is above the cube. I also noticed that if I were to pan the camera to the extreme right or left, the bigger plane would never become one point perspective. So can you explain if this program is accurate? Furthermore, when the cube is on the eye line and facing directly towards me, the width between the left and right vertical lines often exceeds the measurement of the cube's side length. So if I used 2 D perspective and drew the same cube throughout, I would be able to draw 1 main vertical line (which reduces in length as it strays from the middle of the eye line, right?) and 2 pairs of horizontal lines going towards the vanishing points that are set. How can I determine the width between the left and right vertical lines? Also, are the width between these lines constant if draw at different positions with the same vanishing points? (probably not if placing a cube on a vanishing point results in 1 point perspective, right?)

Also, I'm not sure if I understand what you mean by curved guidelines. Would they be like the fish eye example?Thanks!!!

The programs, sketchup included, are accurate. However, the phenomenon you are experiencing is due to the rules of perspective system. The vanishing points are infinitely far away, so if you were to pan the scene, you would need to pan infinitely far away and even then it wouldn't be the one point perspective you are looking for.

That's simply because that vanishing point won't be in front of you until you take a look at it or rotate the cube. When you do, the whole perspective view will change. There is a way to see this happening in sketchup. Simply make a cube and make some guidelines going along the edges. When you rotate the cube, the guidelines will rotate as well, indicating the placement of the vanishing point you are looking for. Here is an example I made some time ago: dl.dropboxusercontent.com/cont…

Besides, one point perspective is merely a simplification and works in certain scenes where the effects of the other vanishing points can be neglected. In reality there are vanishing point in every point you are looking at. However, we base our perception on our surroundings, like a room (I call this global perspective). Thus you will be basing your view on this room, which will have 6 vanishing points because there are 3 dimensions in 3D and each axis has one vanishing point at the end. You will only see as much as you can fit in your field of view though.

There can be only one vanishing point directly in front of you at any time. That's because the other 5 vanishing points are literally on the left, right, below, above and behind you. That said, you need to turn before you can see them, the same apply on sketchup and other programs as well. This will cause interesting things on 2D plane though. In order to show more vanishing points on a drawing, you need to rotate the eyes of the beholder towards the vanishing point in your drawing. This will cause a panorama view like here: www.fortlauderdaleobserver.com… . You know the road is straight, but it's still arcing in the image. This is what I mean with the curved perspective guidelines. In order to show vanishing points on the left and right and to make the guidelines recede towards the vanishing points, they just need to curve like that to emulate the missing third dimension. See more in this tutorial:

There are ways to determine the relative sizes of the edges/faces, but that involves constructing perspective which I'm not fond of. To me constructed perspective feels too rigid and limited, although it has its uses. I prefer curved perspective because that's how we would really see the scene in front of us. For me it's more important the cube "feels and looks like a cube" rather than it being mathematically correct. Anyway, here is an example how to construct perspective: www.automotiveillustrations.co…

So can I try to summarize this all:We see objects in 6 point perspective. Though would you apply them always to your drawings? And is 5 point perspective just one point perspective but with curved guide lines all around like in a sphere shape.

So how big is the field of view for drawing a regular scene. I don't want to draw panoramas but just what we see, but in this 5 point perspective picture s-media-cache-ak0.pinimg.com/o…, we wouldn't be able to actually see this much. So to conclude, we would only use the curved guidelines like that in the photo, but much smaller as in we won't be able to see the vanishing points. And since the objects vanish left right up down and in front, any object that moves away from the center would mean that they would shrink in size (ignoring moving towards and away). But would you draw someone walking perpendicular to you shrinking as they walk further from you? That seems weird even though it makes sense to my eyes. However, when I watch anime, people don't shrink as they walk on a road with a still camera.

This is confusing. Hopefully, you can help me draw a cube in 9 different spots of a page with the same vanishing points without rotating or zooming. I really thought that this was the first step of drawing what we see.

I always apply 6 point perspective in my drawings. However, the amount of distortion depends on the distance between the beholder and the object. It will determine how much the beholder needs to move her eyes to see the object/scene. The more movement required, the more distortion will take place.

Humans have field of vision of ~120 degrees, but you as the artist determine the focal and how much you want to fit within the canvas. Then it's up to you to decide whether you can deal with the limitations of constructed perspective or if you want to apply more real distortion. When the target isn't extremely close to the beholder, distortion can be neglected, making 1-3 point perspective a viable choice. If you want immersion, then small distortion will do the trick. And yeah, we normally can't see as much as shown in the 5-point perspective example.

In any event, if someone is walking away from you, be it a perpendicular or parallel path in relation to where you are looking at, that person will still move away from you and therefore shrink. It feels weird only because of the conversion between 3D and 2D. It just works that way and when you can accept that, perspective is relatively simple. However, you can't make any conclusions based on anime. First and foremost, anime is all about simplification. As long as the character appears to be walking, there may not be any need to take everything in account. The animators save a lot of effort by doing it that way and they sill achieve acceptable results.

So when you say move her eyes, do you mean turning the head. In the example of the distorted table, did you apply distortion because normally you would only be able to see a smaller portion of the table but when you turn your head (or eyes?) you are then able to see the left and right sides of the table, and thus that's why you applied distortion to a close object, right? And you wouldn't apply it to an object farther away because you wouldn't need to turn your head/eyes, right?

Yes, I mean just that. Constructed perspective doesn't take that eye movement in account, and that's its greatest strength and weakness. If there isn't movement and distortion, the lines will be straight and easy to construct with guidelines. Therefore 1,2 and 3 point perspective will work as long as you don't try drawing anything that would require eye movement, because they are beyond the limitations of the static perspective system.

Also, I think that if I were to just draw a cube in the center between the two vanishing points and drew a random vertical lines and two pairs of horizontal lines... Would those horizontal lines be the original height of the cube but at different positions (left or right of the center)? And if this is so, drawing a cube on the vanishing point would be invisible?

Or would the line from the other vanishing point create the new front face? Kinda like in this perspective grid although I don't really understand them ... www.thedrawingwebsite.com/wp-c…

What I mean is do the green lines at for example, the right vanishing point become the new face? And if so, I would have thought that the height of that vertical line would be shorter than the one in the center of the two vanishing points.

I have a question regarding one of the rules of perspective, I've read over a few sites that one rule is that you need to have a 45 degree angle present on the grid, why is that and how would you go about measuring that type of angle accurately?

I actually think I interpreted it wrong, here is the rule I am talking about:

Rule 6: All horizontals which are at 45° to the picture plane are drawn to the point of distance.

I assume that the point of distance means the vanishing point but why does the 45 degree angle rule apply to it? isn't any angle able to go towards the vanishing point?

Also another question, is it required to necessarily draw in the vertical lines in perspective? I heard that it's only use is either to be used in 3 point perspective or make sure that things are straight.

What I do now is do thumbnail sketches of perspective and make sure that the vanishing points are outside of the thumbnail itself and are farther a part from each other, although I had some people tell me on Sycra forums that the vanishing points are too close together, how farther a part would it be good enough to put the vanishing points from each other? is it just a guessing game?